Question 821393: On a recent trip Sarah's car traveled 20 mph faster on the first 130 miles than it did on the remaining 80 miles. The total time for the trip was 4 hours. Find the speed of Sarah's car on the first part of the trip.
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
t = d / s
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stage1:
x = 130/s
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stage2:
y = 80/(s - 20)
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total time = 4 = x + y
4 = 130/s + 80/(s - 20)
4 = 130(s - 20)/s(s - 20) + 80s/s(s - 20)
4s(s - 20) = 130(s - 20) + 80s
4ss - 80s = 130s - 2600 + 80s
4ss - 290s + 2600 = 0
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the above quadratic equation is in standard form, with a=4, b=-290, and c=2600
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4 -290 2600
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the two real roots (i.e. the two x-intercepts), of the quadratic are:
s = 62.0194102
s = 10.4805898
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recall that speed on stage2 is (s - 20), so the second root (s ~= 10.48) would make the speed for stage2 negative (10.48 - 20), which doesn't make sense, therefore, we use the first root (s ~= 62.02)
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answer:
the speed of Sarah's car on the first part of the trip = 62.02 mph
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